To determine the amount of heat produced when 4g of hydrogen gas is burnt, we can use the concept of molar mass and stoichiometry.

Given:

1 mole of hydrogen gas (H?) burns to give 290 kJ of heat.

Step 1: Calculate the number of moles of hydrogen gas in 4g:

The molar mass of hydrogen (H) is 1 g/mol. Since hydrogen gas (H?) has two atoms of hydrogen, its molar mass is 2 g/mol.

To calculate the number of moles, we divide the given mass by the molar mass:

Number of moles = mass / molar mass

Number of moles = 4g / 2 g/mol

Number of moles = 2 mol

Step 2: Calculate the heat produced for 2 moles of hydrogen gas:

Given that 1 mole of hydrogen gas produces 290 kJ of heat, we can calculate the heat produced for 2 moles:

Heat produced = 290 kJ/mol * 2 mol

Heat produced = 580 kJ

Therefore, when 4g of hydrogen gas is burnt under the same conditions, the amount of heat produced is 580 kJ.

So, the correct answer is 580 kJ.